Site-owned videos: Using the YouTube APIs, you can upload all user videos into your YouTube account. In essence, you will own these videos, and your users should be made aware of this. Once the videos are uploaded, you can query and embed them into your site using the YouTube embedded player.

Well-known member

As a follow up to this, perhaps the xenforo 'page' node type would be an ideal place to add such a feature like this, as you can restrict access to it already without any hassle, and it would be just a form the user needs to have access to.